Cherenkov Radiation (and other shocking waves).

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Cherenkov Radiation (and other shocking waves).
Shock Waves May Confuse Birds Internal Compass
Perhaps also the ones of the fish?
http//www.newscientist.com/lastword/answers/lwa67
4bubbles.html http//www.pbs.org/wgbh/nova/barrier
/
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The density effect in the energy loss is
intimately connected to the coherent response of
a medium to the passage of a relativistic
particle that causes the emission of Cherenkov
radiation.
Calculate the electromagnetic energy flow in a
cylinder of radius a around the track of the
particle.
a
Define
If a is in the order of atomic dimension and
laltlt1 we will then get the Fermi relation for
dE/dX with the density effect. If lagtgt1 , we
get (after some steps)
subscript 1 along particle velocity 2, 3
perpendicular to
If l has a positive real part ? the integrand
will vanish rapidly at large distances ? all
energy is deposited near the track If l is purely
imaginary ? the integrand is independent of a ?
some energy escapes at infinite as radiation ?
Cherenkov radiation and
or
and
we assume e real as from now on
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Let us consider a particle that interacts with
the medium
Conservation of energy and momentum
The behavior of a photon in a medium is described
by the dispersion relation
Argon at normal density
W.W.M. Allison and P.R.S. Wright
RD/606-2000-January 1984
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A particle with velocity b bv/c in a medium
with refractive index n nn(l) may emit light
along a conical wave front.
The angle of emission is given by
and the number of photons by
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cos(q) 1/bn m p/bg Dm/m (Dp/p)2
(g2tgqDq)2½ set n 1.28 (C6F14) Dp/p2 51
0-4 Dq 15 mrad L 1 cm 1/l1 -1/l2 1/2200 -
1/1800 (l in A) with Q20
qmax 38.6 o bmin .78
p
K
p
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Threshold Cherenkov Counter
Cherenkov gas
Particle with charge q velocity b
Spherical mirror
Flat mirror
Photon detector
To get a better particle identification, use more
than one radiator.
Positive particle identification
A radiator n1.0024 B radiator n1.0003
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Directional Isochronous Selfcollimating Cherenkov
(DISC)
More general for an Imaging Detector
Cherenkov radiator nf(photon energy)
N photons Nf(b)
200nm 150
(n-1)106
b
Transformation Function
rf(b,n) D(r)f(resolution)
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The light cone
The Cherenkov radiator
Q, b
The particle
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http//banzai.msi.umn.edu/leonardo/
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Detector
Focusing Mirror
Cherenkov media
e-
e
Proportional Chamber
g
g
g
Quartz Plate
e
e
e
E
Photon to Electron conversion gap
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Particle Identification with the DELPHI RICHes
Liquid RICH
Cherenkov angle (mrad)
Gas RICH
p (GeV)
From data p from L K from F D p from Ko
http//delphiwww.cern.ch/delfigs/export/pubdet4.ht
ml
DELPHI, NIM A 378(1996)57
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More beautiful pictures (which has next to
nothing to do with) Cherenkov radiation
ABB.com
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An exact calculation of Transition Radiation is
complicated J. D. Jackson (bless him) and he
continues
A charged particle in uniform motion in a
straight line in free space does not radiate A
charged particle moving with constant velocity
can radiate if it is in a material medium and is
moving with a velocity greater than the phase
velocity of light in that medium (Cherenkov
radiation) There is another type of radiation,
transition radiation, that is emitted when a
charged particle passes suddenly from one medium
to another.
If elt1 no real photon can be emitted for an
infinite long radiator. Due to diffraction
broadening, sub-threshold emission of real
photons in thin radiators.
w02plasma frequency 2 ? (electron density)
If wgtgtw0
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If wp2gtwp1 then Qmax ? g-1
Total radiated power S ? 10-2 g (eV) ? which is
a small number
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Periodic radiator for Transition Radiation.
Coherent addition in point P
(-1)k The field amplitude for successive
interfaces alternate in sign A(Qk) Amplitude fk
w(R/c-t) phase factor
g 2 104 l1 25 mm l2 0.2 mm polypropylene -
air
Egorytchev, V Saveliev, V V Monte Carlo
simulation of transition radiation and electron
identification for HERA-B ITEP-99-11. - Moscow
ITEP , 17 May 1999.
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Production with multi foils
saturation effect due to multi layer
Absorption in foils
w ? 10 keV
Conversion
X radiation
d-electron
MIP
Pulse Height
Threshold
t0
tT
M.L. Cerry et al., Phys. Rev. 10(1974)3594